Method and apparatus for compressing and expanding gases



Oct. 12, 1954 G. A. UNGAR 2,691,432

METHOD AND APPARATUS FOR COMPRESSING AND EXPANDING GASES Original Filed April 25, 1946 16 Sheets-Sheet l INVENTOR GUSTAVE A. UNGAR DECEASED, By

\RMA UNGAR, AOMINISTRATRIX by HM eah ATTORNEYS Oct. 12, 1954 e. A. UNGAR 2,691,482

METHOD AND APPARATUS FOR COMPRESSING AND EXPANDING GASES Original Filed April 23, 1946 '16 Sheets-Sheet 2 INVENTOR 6 u s TAVE A U u GAR. gcms v By lRMA UNGAR,ADM\MISTRATRIX BY MMQ M ATTORNEYS Oct. 12, 1954 G. A. UNGAR 2,691,482

I METHOD AND APPARATUS FOR COMPRESSING AND EXPANDING GASES Original Filed April 23, 1946 16 Sheets-Sheet 3 R: I R

IQMA UNGAR, ADMmu STRATQDQ Y WM MW ATTORNEYS 1954 e. A. UNGAR METHOD AND APPARATUS FOR COMPRESSING AND EXPANDING GASES l6 Sheets-Sheet 4 Original Filed April 23, 1946 XNVENTOR GUSTAVEAU NGAQ, Dec EAseoay, \RMA UNGAR, AommsTRA-rmx FIG.|3

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ATTORNEYS Oct. 12, 1954 G. A. UNGAR 2,691,482

METHOD AND APPARATUS FOR COMPRESSING AND EXPANDING GASES Original Filed April 25, 1946 16 Sheets-Sheet 5 [1 FIG. l5

ATTORNEY S 16 Sheets-Sheet 6 G. A. UNGAR FIG. I?

Oct. 12, 1954 METHOD AND APPARATUS FOR COMPRESSING AND EXPANDING GASES Original Filed April 2:5, 1946 I- J; 4 0/ w I I l FIG. I6

I ENTOR GUSTAVE' AUN Q ,n ace-A520 By \QMA UNGAQ,ADMIN|STQATR|X Y Wat/4w 54w ATTORNEYS Oct. 12, 1954 ca. A. UNGAR 2,591,482

METHOD AND APPARATUS FOR COMPRESSING AND EXPANDING GASES Original Filed April 23, 1946 16 Sheets-Sheet 7 FIG. 20

INVENTOR 605 TAVEAUNGAR, DECEASED By \RMA UMGAQ ,AoMumsTQ ATmx Y Wren or W ATTORNEYS Oct. 12, 1954 G. A. UNGAR 2,691,482

METHOD AND APPARATUS FOR COMPRESSING AND EXPANDING GASES Original Filed April 23, 1946 v 16 Sheets-Sheet 8 I I a- 22A i v i Y I 22A I09 I03 I no F IOI'I9B I06 I7 I INVENTOR GUSTAVE A-UNGAR ,OEc EAsEn By \RMA U NGAR ADM|N|5T RA-rczm ATTORNEYS G. A. UNGAR Oct. 12, 1954 METHOD AND APPARATUS FOR COMPRESSING AND EXPANDING GASES l6 Sheeis-Sheet 9 Original Filed April 23, 1946 FIG.26

FIG. 27

FIG.25

INVENTOR G us'rAVs. AUNGARJEGEAfiE 5 IRMA UN GAR, A DMlm STRAT mx ATTORNEYS Oct. 12, 1954 G. A. UNGAR 2,691,432

METHOD AND APPARATUS FOR COMPRESSING AND EXPANDING GASES 16 Sheets-Sheet 10 Original Filed April 23. 1946 INVENTOR Gus-FAVE A-UNGAQ ,oeae szo By IRMA UNGAR .AOM lNlSTRAT Rux ATTORNEYS G. A. UNGAR Oct. 12, 1954 METHQD AND APPARATUS FOR COMPRESSING AND EXPANDING GASES Original Filed April 23, 1946 16 Sheets-Sheet 11 FIG. 30

FIG. 3| A INVENTOR Gus Ava A-UNGAQ- DecEAseo by \QMA UN6AQ,ADM|NISTRATR\K ATTORNEY S G. A. UNGAR Oct. 12, 1954 METHOD AND APPARATUS FOR COMPRESSING AND EXPANDING GASES l6 Sheets-Sheet 12 Original Filed April 23, 1946 FIG. 35

FIG. 34

' INVENTOR GUs AV A.L) \RMA UN6AQ,A

NGA\2,DECEASED a7 ow u sT zAT mx 5 ATTORNEY 5 Oct. 12, 1954 UNGAR 2,691,482

METHOD AND APPARATUS FOR COMPRESSING AND EXPANDING GASES Original Filed April 25, 1946 16 Sheets-Sheet l W 1am FIG. 37

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*INVENTOR 6u5TAo E AUNGAR, oEcEAsED 5y ATTORNEYS 16 Sheets-Sheet l5 ATTORNEYS Oct. 12, 1954 a. A. UNGAR METHOD AND APPARATUS FOR COMPRESSING AND EXPANDING GASES Original Filed April 25. 1946 w p R s m M m E E R Ow @E l T W. o M V? R. T M M .N. W W s 09 on film o o M m A n E R 00. w M W T S W 33 M on -oo-" -02" loo." mikme 5m Ewi g ww A mfim Mum: Fafimrw A. I E fihdmmrnos V m mas- Eowfimmrwh 2E: fifimmmmrww E owowi ms n \f 09 -O z moso $351523 up G. A. UNGAR Oct. 12, 1954 METHOD AND APPARATUS FOR COMPRESSING AND EXPANDING GASES 16 Sheets-Sheet 16 Original Filed April 23, 1946 INVENTOR. GUSTAVE A.UN6AQ oEceAseo By E M UN6AR,AoM|N|$1-RA-rr2\x By 77%! W A TTORNE Y S Patented Oct. 12, 1954 METHOD AND APPARATUS FOR COMPRESS ING AND EXPANDING GASES Gustave A. Ungar, deceased, late of New Rochelle, N. Y., by Irma Ungar, administratrix, New Rochelle, N. Y., assignor to Equi-Flow, Inc., New York, N. Y., a corporation of Delaware Substituted for abandoned application Serial No. 664,255, April 23, 1946. This application July 17, 1952, Serial No. 299,766

18 Claims. 1

This invention relates to a new and improved method and apparatus for producing the polytropic and non-polytropic compression and the polytropic and non-polytropic expansion of a gas or mixture of gases. The invention relates particularly to polytropic compression and expansion.

This application is a substitute for abandoned application Ser. No. 664,255, filed April 23, 1946, by Gustave A. Ungar.

According to this method, rotary compressors can be used, which may be of any positive-displacement type.

Such rotary compressors are well-known, but they are suitable only for low compression ratios, because of their low thermal efliciency at high compression ratios.

For example, in the lobe or Root type of rotary compressor, which includes gear pumps, the gas is drawn in at an inlet pressure into the apparatus, in successive pockets. Each pocket is delivered to the outlet of the apparatus, which is connected to a storage tank, at the initial inlet pressure of the gas. As each pocket thus communicates with the storage tank at the outlet end of the compressor, there is a rush of gas or air from the tank into the respective communicating pocket of the compressor, because the pressure in said tank is higher than the initial inlet pressure. The entry of the compressed air of the tank into the respective communicating pocket results, in effect, in an increase of pressure of the gas in the pocket, at constant volume.

It has been attempted to diminish this undesirable effect in compressors of the Root type and vane type, by providing means for reducing the volume of the drawn-in gas volume, before establishing full communication between the respective pocket of the compressor and the storage tank. Such known design requires a considerable reduction in the size of the discharge port between the compressor and the storage tank, unless a low compression ratio is used. This reduction in port size produces wire drawing or throttling losses.

In such known design, the best compression ratio has been 3.5 to 1. A higher compression ratio resulted in excessive wire-drawing or throttling losses, due to greatly reduced area of the discharge port of the compressor. According to this invention, a compression ratio of 5 to 1 can be secured, and even higher, with high efliciency, and with the elimination of said losses.

In using a rotary compressor of the conventional vane type, a somewhat higher compression ratio can be secured than in the Root type.

However, reduced discharge port area in the vane-type compressor also produces throttling losses. Likewise, a high compression ratio produces mechanical difficulties, because the vanes slide under heavy loads in the rotor slots. It is also necessary to provide pressure unloading devices before the pressure in the storage tank approaches the desired maximum pressure. Otherwise, there is a possibility of vane fracture, due to excessive overload.

Another disadvantage of each existing type of positive-displacement rotary compressor, is that each said compressor is designed to produce a fixed and selected compression ratio, and it is designed to deliver a fixed and selected end-pressure. If the same compressor is used for producing a different end-pressure than the selected end-pressure, there is a loss of efficiency unless the outlet port of the compressor is modified.

According to one embodiment of this invention, each charge of gas is compressed in a compression space or chamber which is provided intermediate or between a set of primary rotors and a succeeding set of secondary rotors. Both sets of rotors are continuously driven, and the compression is secured because the input displacement of the set of primary rotors is more than the delivery or output displacement of the set of secondary rotors. A polytropic compression can thus be secured in said intermediate compression chamber. In this embodiment, the apparatus delivers pockets of the gas, at its final pressure and temperature, to the secondary set of rotors, which then deliver the compressed gas to the storage tank, without any change of pressure or temperature in said secondary rotors. The final pressure which is produced in the intermediate compression space or chamber, may be the selected maximum pressure which it is desired to produce in the storage tank. Wire-drawing or throttling losses are thus eliminated, because an outlet port of ample size for the compressor can be used, and because the compressed air is discharged from the. outlet of the secondary rotor in a substantially continuous and uniform stream with constant pressure.

An intermediate compression space or chamber can also be provided, whose minimum selected volume can be regulated, either manually or automatically, during the operation of the device. If the minimum volume of the compression chamber remains fixed, such apparatus operates with maximum efiiciency if it is working against a fixed outlet pressure. However, if the compressed gas is forced into a storage tank, the pressure in such tank is gradually increased from an initial pressure to a selected maximum. In using a compressor whose intermediate compression space has a fixed volume, it'is necessary always to create a final pressure in said compression space, which exceeds the selected maximum pressure in the storage tank. This results in low efilciency while the tank pressure is substantially below the outlet pressure of the compressor.

The minimum volume of the intermediate compression space is therefore regulated, so that said minimum volume is decreased as the pressure in the tank is increased. The delivery pressure of the compressor is therefore maintained at a selected value above the transient pressure in the storage tank. The drive of the valve rotors by the compressed gas in the intermediate compression chamber is thus minimized.

Numerous additional objects and advantages of this invention are set forth in the annexed description and drawings, which illustrate preferred embodiments thereof.

The first embodiment is illustrated in Figs. 1 and 2, which utilizes the lobe or Root type of rotor, with external lobes.

Fig. 1 is a vertical section on the line l! of Fi 2.

Fig. 2 is a section on the line 2-2 of Fig. 1.

Figs. 3-6 inclusive illustrate the second embodiment, which utilizes the vane type of rotor.

Fig. 3 is a section on the line 3-3 of Fig. 4.

Fig. 4 is a vertical section on the line 4-4 of Fig. 3.

Figs. 5 and 6 are respective sections on the lines 5--5 and 6-45 of Fig. 3.

Figs. 7-9 inclusive illustrate the third embodiment, which utilizes a helical type of rotor, in which the intermediate space or chamber is of zero volume.

Fig. 7 is a vertical section, partially in elevation, showing the helical rotors.

Fig. 8 is a section on the line 8--8 of Fig. 9.

Fig. 9 is a section on the line 9--9 of Fig. 8.

Figs. 1c and 11 illustrate the fourth embodiment which is a multiple stage compressor.

Fig. 10 is a section on the line Ill-l of Fig. 11.

Fig. 11 is a section on the line I ll I of Fig. 10.

Figs. 12-19 illustrate the fifth embodiment, which illustrates the regulation of the minimum volume of the intermediate space or compression chamber. The compressor uses the lobe or Root type of rotor.

Fig. 12 is a section on the line l2l2 of Fig. 13. Fig. 13, in its lower part, is a section on the line l3l3 of Figs. 12, 16, 17, 18; and in its upper part, beginning with the section line l9l9, is a section on l3A--l3A of Fig. 19.

Fig. 14 is a section on the line l4l4 of Fig. 12. Fig. 15 is a section on the line II5 of Fig. 12. Fig. 16 is a section on the line l6l 6 of Fig. 13. Fig. 17 is a section on the line ll--ll of Fig. 13. Fig. 18 is a section on the line l8l8 of Fig. 13. Fig. 19 is a section on the line i9l9 of Fig. 13.

Figs. 20 and 21 illustrate the sixth embodiment in which the vane type of rotor is used, and the volume of the intemediate compression chamber is regulated by the pressure in the storage tank.

Fig. 20 is a section on the line 20-20 of Fig. 21.

Fig. 21 is a section on the line 2 l-2l of Fig. 20.

Figs. 22, 22A and 23 illustrate the seventh embodiment, in which the primary and secondary rotors can be coupled and uncoupled, by a mechanical or other clutch or coupling means, which may be of any type.

Fig. 22 is a section on the line 2222 of Fig.

22A, which illustrates the automatic coupling of the primary and secondary rotors. This is regulated by the pressure in the storage tank.

Fig. 22A is a section on the line 22A-22A of Fig. 22.

Fig. 23 illustrates a device for manually coupling and uncoupling the primary and secondary rotors.

Figs. 24-31 illustrate the eighth embodiment, which illustrates a reversible motor made according to this invention, so that the power shaft of the motor can be driven in either of two opposed directions. In this embodiment, the use of lobetype rotors is illustrated.

Fig. 24.- is a section on the line 24-24 of Fig. 28.

Fig. 25 is a section on the line 25-25 of Fig. 28.

Fig. 26 is a section on the line 26-26 of Fig. 28.

Fig. 27, in its upper part is a section on TIA-41A of Fig. 28, and in its lower part, it is a section on 21--2l of Fig. 28.

Fig. 28 is a section on the line 28-28 of Fig.

24, and it is also a section on the line 28-48 of Figs. 25, 30, and Fig. 31-31B.

Fig. 29 is a section on the line 29-49 of Fig. 25.

Figs. 30, 3l-31B illustrate the positions of the inner housings of this eighth embodiment, when the motor shaft turns reversely to the direction of Figs. 24-29. Fig. 30 corresponds to Fig. 25.

Fig. 31A is a detail of the rotors of this eighth embodiment.

The ninth embodiment is illustrated in Figs. 32-38, which shows means for varying the compression volume in a vane-type compressor, which can also be used reversely as a motor.

Fig. 32 is a section on the line 32-32 of Fig. 37.

Figs. 33, 34, 35 are respective sections on the respective lines 33-33, 34-34, 3535 of Fig. 36.

Fig. 36 is a section on the line 36-36 of Fig. 33.

Fig. 37 is a horizontal median section of Fig. 33.

Fig. 38 illustrates a manual control for regulating the compression volume, hereinafter designated as V2.

Figs. 39, 40 and 41 illustrate a number of graphs which explain the principle of the invention.

Each type of compressor apparatus made according to this invention, can be used reversely as a motor.

First embodiment Figs. 1 and 2 This is a single-stage compressor system. It comprises primary rotors R and R", and secondary rotors 8 and 9. The two primary rotors R and R" are identical with each other. The two secondary rotors 8 and 9 are also identical with each other. These rotors, R, R", 8, 9, are respectively detachably keyed or otherwise detachably fixed to respective parallel shafts H, 18, 2|, 25. As an example, primary rotor R and secondary rotor 8 are turned clockwise, and primary rotor R." and secondary rotor 9 are turned counterclockwise.

These rotors are of the lobe type or gear type.

The lobes of each set of rotors intermesh, optionally with zero clearance. It is within the scope of the invention to use rotors which are driven through timing gears and whose lobes have small clearance, thus eliminating metal-tometal contact between the lobes of the intermeshing rotors. If such clearances are used it is unnecessary to provide internal lubrication for the rotors. These rotors operate without timing gears when there is zero clearance. However, it

is desirable for some purposes,- to use zero clearance with the necessary internal lubrication of the rotors, in order to reduce volumetric losses which result from even small clearances. Such volumetric losses make it necessary to rotate the rotors at very high anguluar velocity, in order to deliver a substantially continuous and uniform output of compressed air or gas. Such uniform and continuous output is desirable. Any known means can be used, in order to secure internal lubrication.

In this embodiment, the four rotors have the same number of lobes, and they are of the same width, as measured in the direction of the parallel axes of rotation of the respective shafts II, I8, 2|, and 25. In this embodiment, the four rotors are rotated in unison at the same angular velocity, so that each said rotor is turned through the same number of revolutions per minute.

The pitch diameter of the secondary rotors 8 and 9, is less than the pitch diameter of the primary rotors R and R".

These rotors are located respectively in a primary housing H and in a secondary housing I, which are integral.

Primary housing H for the primary rotors R and R has an inlet passage 2. Secondary housing I for the secondary rotors 8, 9 has an outlet IS.

The housings H and I have a common cover I 9, which is fixed gas-tight to said housings by bolts 20. The usual packing can be used, in order to produce a gas-tight connection between cover I9 and said housings H, l.

Respective and equal sprockets 22 and 23 are respectively fixed to shaft I! of primary rotor R, and to shaft 2! of secondary rotor 8.

These equal sprockets 22 and 23 are fixed to parts of shafts I? aond 2I, which extend axially beyond cover I9. These shafts I! and 2| are turned in the same direction.

Chain 24 connects sprockets 22 and 23. Primary rotor R is driven by primary rotor R, and secondary rotor I) is driven by secondary rotor 8.

Each of the housings H and I has respective portions which have internal walls of cylindrical shape.

At these respective cylindrical portions, the

lobes of the primary rotors R and R" form respective sealed primary pockets 4 and 3, and the lobes of the secondary rotors 8 and 9 form respective sealed secondary pockets II and I2.

Each primary pocket and 3 is filled with gas at the inlet port 2, at the inlet pressure P1 of the gas. Each pocket 4 and 3 conveys a respective gas-pocket at pressure P1 to the intermediate space or chamber I6, through which the gas is transferred to the secondary rotors 8 and 9.

The gas which is delivered from the space or chamber Ii] to the secondary pockets II and I2, is at the maximum pressure P2 which is produced in the apparatus, so that chamber I0 is a compression chamber.

Each cycle of operation of the apparatus is performed, while the rotors turn through equal respective angles, which are defined by the respective and angularly equal arcs 6, 5, I4, I5.

The gas or air is compressed in the intermediate space Ill, in each of said series of consecutive cycles. Each volume V2 of compressed gas which is produced in each cycle at pressure P2 is delivered at volume V2 and pressure P2 to a respective pair of secondary pockets, which deliver the same atvolume V2 and pressure P2 to outlet It. Said outlet I6 ;may'be connected to the'inlet of a storage tank. Said tank may be maintained sealed, save at its connection to outlet I6, so'that the pressurein the tank is progressively increased to. a selected maximum. If desired, the tank may have an outlet which is opened by a regulating valve while compressed gas is supplied to the tank, so that the pressure in the tank is maintained at a constant selected pressure, after they pressure in the tank has been increased to said selected value. Outlet I5 may beconnected to anatomizer or other apparatus which directly utilizes the current of compressed gas which flows through outlet I6.

The rotors are preferably rotated at high velocity. Hence, although the apperatus delivers consecutive volumes V2 of compressed gas at pressure P2 to outlet IS, a substantially uniform current. of gas, flowing at substantially uniform velocity, can be supplied to outlet I6.

Fig. 1 shows the respective positions of the four rotors, at the end of a respective cycle. At this stage,v the volume of the intermediate space II) is of minimum volume V0, and the air or gas in said intermediate space It] is at the maximum pressure P2. This is the end-compressionstage of the respective cycle.

At this end-compressionstage, the respective primary pockets 4 and 3,,Whl0h are located at the stations 4a and 3a, and which are directly adjacent the intermediate space III, are sealed from said intermediate space It and from the other, pockets 2 and 3 and from the inlet 2. At this end-compression stage, the, respective secondary pockets II and I2 at the respective stations 8a and 8b, which are directly adjacent the inter mediate space It, are also sealed from said intermediate space Ill and from the other pockets II and I2 and from the outlet I6.

At this end-compression stage, the secondary pockets II and I2 which are directly adjacent the outlet It in Fig. l aresealed from said outlet I6. .In the preferred embodiment, and as previously stated, there is a substantially continuous and uniform flow of gas through the outlet 16, in the direction of the arrow in Fig. 1. Said outlet It may be connected to an outlet pipe of any desired length, whose internal diameter may be equal to the diameter of outlet I6, whose internal wall may be cylindrical. The diameter of said outlet pipe may'bear any relation to the internal diameter of outlet IS. The cross-section of outlet I6 may remain fixed, and the cross-section of the connection or connections which succeed outlet I6 may remain fixed.

During each cycle, the primary rotors R. and R force into said intermediate space III, a volume V1 of gas at inlet pressure P1, and said volume V1 is equal'to twice thevolume of a primary pocket ier 3.. The compressed gas volume V2 which is discharged into outlet it at pressure P2 during each cycle, equals twice the volume of a secondary pocket II and I2. The inlet'pressure P1 may be external atmospheric pressure.

Assume that the rotors are rotated through a small angle in advance of their respective endcompression positions of Fig. l, in the directions of the respective arrows.

Intermediate space III will then communicate with the two adjacent primary pockets 4 and 3,

which are turned through said small angle to wards said intermediate space I Ii. The minimum volume Vc of'intermediate space I 0 which is shown in Fig. 1, will be thus increased to V0 plus- Vi. This will result in a sharp" drop'in pressure in the intermediate space H1; because the=compressed air or gas therein whichis at the maximum pressure P2 atminimum volume V in Fig. 1, will be intermixed with the two volumes of gas, namely, volume V1, of the adjacent pockets 4 and 3 at the stations ia and3ar, to produce a mixture pressure Fe. The secondary pockets at the stations Ba!r and 8b will remain sealed from said intermediate space to when the rotors are turned; through said small angle. because said secondary pockets H and [2 are turned away from. said space Hi. The secondary'pockets H and t2 which are adjacent the outlet IS in Fig. 1, will discharge their respective volumesofairor gas when. the rotors are turned through said small angle, atthe maximum pressure P2 which is produced in space I0, into the outlet IS. The volume of compressed'gas which is thus discharged is volume V2.

After this mixing step which occurs at the beginning of each cycle,- together with a simultaneous discharge of a volume V2 of compressed gas at pressure P2 at the outlet 16, the air or gas in space-ill is compressed to the maximum pressure P2 by the further rotation of the rotors during the respective cycle, and the secondary pockets i l and 2 at stations Baand. 8b are sealed from the space [0, just at the end of the respective cycle, which is the end-compression stage. Hence each sealed secondary pocket receives and retainsa charge or volume of air at the maximum pressure P2, until the respective volume V2 is discharged at pressure P2 into the outlet 16.

Fig. 39 shows two sets of graphs respectively in full and broken lines, which illustrate the ad-' vantage. of using an intermediate space H} which has lowest minimum volume Vc, at the end-compression stage of Fig.1.

In each. set ofv graphs, the abscissa denotes volume in cubic inches, and; the ordinate indicates" pressure in'pounds per square inch.

In. the ideal isothermal cycle which it is preferred to approach as closely as possible in compressing a gas, n equals 1. In the broken-line set 01'. graphs; n equals 1.1, and 1:. equals 1.3 in the full-line set. i The symbol n is the exponent in the well-lmown equation for the polytropic change of stateof perfect gases, namely, po"=constant.

V0 is the minimum volume in. cubic inches. of the intermediate space I 0, as shown in Fig. 1. at the end of thecompression stage. This is the minimum value of the volume of said intermediate space ill. The broken-line raphs in Fig. 39 correspond to respective valuesof Vc, of 50, 80, 100,150, 200' cubic inches. The bottom broken line graph correspondsto a value of V0 of 56 cubic inches.

The four full-line graphs in Fig. 39 correspond to respective values of Va, of 50,100, 150, ZOO-cubic inches;

In each set of graphs, V1, which represents twice the volume of a primary pocket 4 or 3, equals 100 cubic inches. This is the inlet volume at inlet pressure P1, which may be normal atmospheric pressure or of any value.

V2 represents twice the volume of a secondary pocket I l or l2. In the broken-line set of graphs, V2 equals 23.45 cubic inches. In the full-line set of graphs, V2 equals 28.99 cubic inches. These are the respective outlet volumes at pressure P2 which are delivered to the outlet. The graphs of: Figs. .40 and. 41 show the efiect of increasing.

mean temperature with increasing Vc-,.- for; 'n-

8. equaling 1.1 and l.3 respectively. It is clear that an increase in mean temperature should be avoided, for highest efficiency.

The economy in power consumption increases as Vc is diminished.

If the pressure in the storage tank T exceeds Pi, and assuming that the air or gas is passed through the apparatus and said air or gas is delivered to tank T without increasing its pressure aboveinlet pressure P1 there is maximum power consumption and minimum efiiciency.

Calculating the power consumption as under such condition of minimum efiiciency, said maximum power consumption of 100 is reduced according to the respective values of V0 as follows, if n=1.1:

Volume of V'c in Cubic Inches The power consumption also increases, as the value of the coefiicient n is increased. Hence 12 should approach 1 as closely as possible, by removing heat during the compression, to approach the ideal isothermal compression as closely as possible.

One function of the secondary rotors is to seal the outlet Hi from the intermediate space H3, or from the primary rotors, if said space It has zero volume. Hence the secondary rotors operate as valves.

If the pressure in the storage tank isv gradually built up from P1, for example, to a selected maximum tank pressure, the secondary rotors are driven continuously by the gas pressure which is created by the difference between input displacement and output displacement in space 60, as long as the pressure in the storage tank does not exceed the mixing pressure Pc.

When.- the pressure in the storage tank equals or is less than the mixing pressure Pc, mechanical driving force is required to operate the secondary rotors, and said driving force is provided by connecting the shaft i! to a motor, and by the sprocket and chain connection previously stated. When the pressure'in the tank exceeds the mixing pressure Po, there will be a part of each cycle during which the pressure in space 10 will exceed the pressure in the storage tank. During such part of each cycle, the compressed gas or air in space ill will supply motive power to the secondary rotors.

One of the great advantages of my invention is that all the pressure variations which result from the difference in the respective displacements, take place in advance of the outlet 16. Such pressure variations are wholly confined to the space I0. In any event, they do not take place at outlet [6, save for the pressure variation which occurs because P2 exceeds the transient tank pressure.- The pockets of compressed gas, which constitute volumes V2, are discharged from the secondary pockets at constant pressure P2 into thenoutlet [6..- This advantage exists if the outlet [-6 is the inlet of an atomizer or other device, instead of being the inlet of a storage tank.- By rotating the rotors at. high angular velocity, the respective volumes V2 of compressed 

